I agree its complicated, but it has significant impact day to day, is never talked about, and has the most untapped potential as a reef keeping tool.
The best way to explain it is;
When iron rusts it is being atomically reduced, and its solid state is being changed.
Bleach or peroxide removing color from hair, clothing, etc, are other examples of radical oxidation.
Oxidizing is basically rust, but instead of iron, oxygen and other oxidizers (there are many different oxidizing molecules) are reducing dead organics atomic state. (It also effects other materials in the system, but at a MUCH slower rate)
There is a constant balance between organics present, and oxidizers present, and you never want to have the balance too far on either side, but the ratio will effect water clarity, nutrient levels, and thus animal behavior and growth. Live animals are also sensitive to these levels, and changes should be made very slowly.
This is a tool used by many public water sanitation systems, and is the sole motivation for dosing ozone.